Question

Suppose we have a spaceship about the size of a typical ocean cruise ship today, which means it has a mass of about 120 million kilograms, and we want to accelerate the ship to a speed of 12 % of the speed of light. Suppose you want to generate the energy to get it to cruising speed using matter-antimatter annihilation.
Part A. How much energy would be required? (Hint: You can find the answer simply by calculating the kinetic energy of the ship when it reaches its cruising speed; because 12 % of the speed of light is still small compared to the speed of light, you can use the formula that tell us that kinetic energy = 12mv2.) Express your answer using two significant figures.
Part B. How does your answer compare to total world energy use at present, which is about 5×1022 joules per year? How does your answer compare to total world energy use at present, which is about joules per year? EspaceshipEworldenergyuse∼1 EspaceshipEworldenergyuse∼105 EspaceshipEworldenergyuse∼1020
Part C. The typical cost of energy today is roughly 5¢ per 1 million joules. Using this price, how much would it cost to generate the energy needed by this spaceship? Express your answer using two significant figures.

Answer 1

Answer:   A 7.8 ·10^22 J  B   1.6 times  C 3.9 ·10^15 $

Explanation: A : Speed of light c =  3.0·10^8 m/s,  0.12·c = 3.6·10^7 m/s  

Mass is 120·10^6 kg . Change of kinetic energy

E = ½mv² =  0.5 · 120·10^6 kg · (3.6·10^7 m/s)² = 7.776·10^22 J

B  exponent is same , 7.776 / 5 = 1,55 times of energy use of Earth in year.

C  Energy is  7.776·10^22 J / 10^6  = 7.776·10^16 MJ

Price is 0.05 $ · 7.776·10^16 MJ = 3.888·10^15 $

Answer 2

A. The energy required to get to the cruising speed is 7.8×10²² J

B. The energy needed will be 1.56 times the total world energy

C. The cost price required to generate the energy needed by the spaceship is $ 3.9×10⁵

A. Determination of the energy

Mass (m) = 120×10⁶ Kg

Velocity of light = 3×10⁸ m/s

Velocity of spaceship = 0.12 × 3×10⁸ = 3.6×10⁷ m/s

Energy (E) =?

E = ½mv²

E = ½ × 120×10⁶ × (3.6×10⁷)²

E = 7.8×10²² J

Thus, the energy needed is 7.8×10²² J

B. Comparing the energy needed to the total world energy.

Energy needed = 7.8×10²² J

World energy = 5×10²² J

Energy needed / World energy = 7.8×10²² / 5×10²²

Energy needed / World energy = 1.56

Cross multiply

Energy needed = 1.56 × World energy

Thus, the energy needed is 1.56 times the World energy

C. Determination of the cost required to generate the energy

1×10⁶ J = $ 0.05

Therefore,

7.8×10²² J = (7.8×10²² × 0.05) / 1×10⁶

7.8×10²² J = $ 3.9×10⁵

Therefore, the cost required to generate the energy is $ 3.9×10⁵

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